Power

``Power(a, b) a ^ b``

represents `a` raised to the power of `b`.

Note: `Power` has the `Listable` attribute and `Power(x,y,z)` is grouped as `x^(y^z)`

You can't do matrix calculations with the `^operator`:

``>> {{2,1},{1,1}} ^ 2``

is computed as:

``{{2^2,1^2},{1^2,1^2}}``

Use `Inverse({{2,1},{1,1}})` or `MatrixPower({{2,1},{1,1}},2)` to calculate matrix inverses and powers.

Don't confuse the `^` operator with the `^^` operator, which can be used for integer number bases other than `10`. Here's an example for a hexadecimal number:

``>> 16^^abcdefff 2882400255``

See

### Examples

``>> 4 ^ (1/2) 2 >> 4 ^ (1/3) 4^(1/3) >> 3^123 48519278097689642681155855396759336072749841943521979872827 >> (y ^ 2) ^ (1/2) Sqrt(y^2) >> (y ^ 2) ^ 3 y^6``

Use a decimal point to force numeric evaluation:

``>> 4.0 ^ (1/3) 1.5874010519681994``

`Power` has default value `1` for its second argument:

``>> a /. x_ ^ n_. :> {x, n} {a,1}``

`Power` can be used with complex numbers:

``>> (1.5 + 1.0*I) ^ 3.5 -3.682940057821917+I*6.951392664028508 >> (1.5 + 1.0*I) ^ (3.5 + 1.5*I) -3.1918162904562815+I*0.6456585094161581``

Infinite expression 0^(negative number)

``>> 1/0 ComplexInfinity >> 0 ^ -2 ComplexInfinity >> 0 ^ (-1/2) ComplexInfinity >> 0 ^ -Pi ComplexInfinity``

Indeterminate expression 0 ^ (complex number) encountered.

``>> 0 ^ (2*I*E) Indeterminate >> 0 ^ - (Pi + 2*E*I) ComplexInfinity``

Indeterminate expression 0 ^ 0 encountered.

``>> 0 ^ 0 Indeterminate >> Sqrt(-3+2.*I) 0.5502505227003375+I*1.8173540210239707 >> Sqrt(-3+2*I) Sqrt(-3+I*2) >> (3/2+1/2I)^2 2+I*3/2 >> I ^ I I^I >> 2 ^ 2.0 4.0 >> Pi ^ 4. 97.40909103400242 >> a ^ b a^b >> Power(x,y,z) Power(x,Power(y,z))``